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Research Article

European option under a skew version of the GBM model with transaction costs by an RBF method

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Pages 2986-3004 | Received 14 Mar 2020, Accepted 04 Apr 2021, Published online: 16 May 2021

References

  • Mandelbrot BB, Van Ness JW. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 1968;10(4):422–437.
  • Heston SL. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud. 1993;6(2):327–343.
  • Mehrdoust F, Najafi AR. Pricing European options under fractional Black-Scholes model with a weak payoff function. Comput Econ. 2018;52(2):685–706.
  • Azzalini A, Capitanio A. Statistical applications of the multivariate skew normal distribution. J R Stat Soc: Ser B (Stat Methodol). 1999;61(3):579–602.
  • Azzalini A, Valle AD. The multivariate skew-normal distribution. Biometrika. 1996;83(4):715–726.
  • Corns T, Satchell S. Skew Brownian motion and pricing European options. Eur J Financ. 2007;13(6):523–544.
  • Richards FS. A method of maximum likelihood estimation. J R Stat Soc: Ser B (Methodol). 1961;23(2):469–475.
  • Petrovski A, Wilson A, McCall J. Statistical analysis of genetic algorithms and inference about optimal factors, No. 1. Aberdeen: Faculty of Science and Technology, School of Mathematics in Computer Science, The Robert Gordon University; 1998. p. 1–20.
  • Giovanardi B, Serebrinsky S, Radovitzky R. A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers. Comput Eng., Financ. Sci. 2020. arXiv:1911.10275v1.
  • RezaeiRad A, Burton HV, Weinand Y. Macroscopic model for spatial timber plate structures with integral mechanical attachments. J Struct Eng. 2020;146(10):04020200.
  • Kulkarni SA, Bajoria KM. Geometrically nonlinear analysis of smart thin and sandwich plates. J Sandw Struct Mater. 2006;8(4):321–341.
  • Leland HE. Option pricing and replication with transactions costs. J Financ. 1985;40(5):1283–1301.
  • Kabanov YM, Safarian MM. On Leland's strategy of option pricing with transactions costs. Financ Stoch. 1997;1(3):239–250.
  • Mehrdoust AR, Farshid N, Fallah S, et al. Mixed fractional Heston model and the pricing of American options. J Comput Appl Math. 2018;330:141–154.
  • Fallah S, Najafi AR, Mehrdoust F. A fractional version of the Cox–Ingersoll–Ross interest rate model and pricing double barrier option with hurst index h (2 3, 1). Commun Stat Theor Methods. 2019;48(9):2254–2266.
  • Li X, Dong H. Analysis of the element-free Galerkin method for Signorini problems. Appl Math Comput. 2019;346:41–56.
  • Yu S, Peng M, Cheng H, et al. The improved element-free Galerkin method for three-dimensional elastoplasticity problems. Eng Anal Bound Elem. 2019;104:215–224.
  • Ilati M, Dehghan M. Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem. J Comput Appl Math. 2018;327:314–324.
  • Jafarabadi A, Shivanian E. Numerical simulation of nonlinear coupled Burgers equation through meshless radial point interpolation method. Eng Anal Bound Elem. 2018;95:187–199.
  • Ghorbani M. Diffuse element Kansa method. Appl Math Sci. 2010;4(12):583–594.
  • Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech. 1992;10(5):307–318.
  • Giannaros E, Kotzakolios A, Kostopoulos V, et al. Hypervelocity impact response of CFRP laminates using smoothed particle hydrodynamics method: implementation and validation. Int J Impact Eng. 2019;123:56–69.
  • Yin J, Shi Z, Chen J, et al. Smooth particle hydrodynamics-based characteristics of a shaped jet from different materials. Strength Mater. 2019;51(1):85–94.
  • Abbaszadeh M, Dehghan M. Direct meshless local Petrov–Galerkin (DMLPG) method for time-fractional fourth-order reaction–diffusion problem on complex domains. Comput Math Appl. 2019;79:876–888
  • Taleei A, Dehghan M. Direct meshless local Petrov–Galerkin method for elliptic interface problems with applications in electrostatic and elastostatic. Comput Methods Appl Mech Eng. 2014;278:479–498.
  • Hosseini VR, Shivanian E, Chen W. Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping. J Comput Phys. 2016;312:307–332.
  • Shivanian E. On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations. Int J Numer Methods Eng. 2016;105(2):83–110.
  • Fornberg B, Flyer N. Solving PDEs with radial basis functions. Acta Numer. 2015;24:215–258.
  • Mirzaee F, Samadyar N. On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions. Eng Anal Bound Elem. 2019;100:246–255.
  • Khattak AJ, Tirmizi S, Siraj-ul-Islam, Application of meshfree collocation method to a class of nonlinear partial differential equations. Eng Anal Bound Elem. 2009;33(5):661–667.
  • Dehghan M, Shokri A. A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions. Numer Algorithms. 2009;52(3):461–477.
  • Cavoretto R, Fasshauer GE, McCourt M. An introduction to the Hilbert–Schmidt SVD using iterated Brownian bridge kernels. Numer Algorithms. 2015;68(2):393–422.
  • De Marchi S, Santin G. Fast computation of orthonormal basis for RBF spaces through Krylov space methods. BIT Numer Math. 2015;55(4):949–966.
  • Fasshauer GE, McCourt MJ. Stable evaluation of Gaussian radial basis function interpolants. SIAM J Sci Comput. 2012;34(2):A737–A762.
  • Fornberg B, Larsson E, Flyer N. Stable computations with Gaussian radial basis functions. SIAM J Sci Comput. 2011;33(2):869–892.
  • Fornberg B, Piret C. A stable algorithm for flat radial basis functions on a sphere. SIAM J Sci Comput. 2007;30(1):60–80.
  • Fornberg B, Wright G. Stable computation of multiquadric interpolants for all values of the shape parameter. Comput Math Appl. 2004;48(5–6):853–867.
  • Larsson E, Fornberg B. Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions. Comput Math Appl. 2005;49(1):103–130.
  • Pazouki M, Schaback R. Bases for kernel-based spaces. J Comput Appl Math. 2011;236(4):575–588.
  • Hardy RL. Multiquadric equations of topography and other irregular surfaces. J Geophys Res. 1971;76(8):1905–1915.
  • Kansa EJ. Multiquadricsa scattered data approximation scheme with applications to computational fluid-dynamics surface approximations and partial derivative estimates. Comput Math Appl. 1990;19(8–9):127–145.
  • Franke R. A critical comparison of some methods for interpolation of scattered data. Monterey, CA: Naval Postgraduate School Monterey; 1979.
  • Goto Y, Fei Z, Kan S, et al. Options valuation by using radial basis function approximation. Eng Anal Bound Elem. 2007;31(10):836–843.
  • Hon YC. A quasi-radial basis functions method for American options pricing. Comput Math Appl. 2002;43(3–5):513–524.
  • Chiogna M. A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution. Stat Methods Appl. 2005;14(3):331–341.
  • Raphson J. Analysis aequationum universalis seu ad aequationes algebraicas resolvendas methodus generalis, et expedita, ex nova infinitarum serierum doctrina. deducta ac demonstrata. Original in British Library, London; 1960.
  • Yalçınkaya A, Şenoğlu B, Yolcu U. Maximum likelihood estimation for the parameters of skew normal distribution using genetic algorithm. Swarm Evol Comput. 2018;38:127–138.
  • Chen S, Gopalakrishnan P. Speaker, environment and channel change detection and clustering via the Bayesian information criterion. DARPA broadcast news transcription and understanding workshop, Vol. 8; 1998; IBM T.J. Watson Research Center, Virginia. p. 127–132.
  • Wendland H. Scattered data approximation; 2005.
  • Micchelli CA. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Construct Approx. 1986;2:11–22.
  • Schoenberg IJ. Metric spaces and completely monotone functions. Ann Math. 1938;39:811–841.
  • Wu ZM, Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA J Numer Anal. 1993;13(1):13–27.
  • Wu ZM. Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs. Chin J Eng Math. 2002;2(2).
  • Kreyszig E. Introductory functional analysis with applications, Vol. 1. New York: Wiley; 1978.
  • Franke R. Scattered data interpolation: tests of some methods. Math Comput. 1982;38(157):181–200.
  • Carlson RE, Foley TA. The parameter R2 in multiquadric interpolation. Comput Math Appl. 1991;21(9):29–42.
  • Rippa S. An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Adv Comput Math. 1999;11(2–3):193–210.
  • Azarboni HR, Keyanpour M, Yaghouti M. Leave-two-out cross validation to optimal shape parameter in radial basis functions. Eng Anal Bound Elem. 2019;100:204–210.

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